Poly (glycerol-sebacate) (PGS) is a synthetic bioelastomer with a covalently crosslinked, three-dimensional network of random coils with hydroxyl groups attached to its backbone. This biodegradable polymer is biocompatible (in vitro and in vivo), tough, elastic, inexpensive, and flexible, and finds potential applications in tissue engineering and regenerative medicine. Due to the slow rate of step-growth polymerisation, the synthesis of PGS prepolymer requires 24-48 h. A batch and a continuous process, if developed, could address the inherent deficiencies (eg. long residence time, venting) associated with the large-scale synthesis of such bioelastomers. However, in order to assess whether this particular system may be adapted to continuous processes, such as reactive extrusion, studies on kinetics of controlled condensation reactions are of vital importance. FT-Raman spectroscopy was used to study the kinetics of the step-growth reactions between glycerol (G) and sebacic acid (SA) at three molar ratios (G:SA= 0.6,0.8,1.0) and three temperatures (120, 130, 140 ˚C). The rate curves followed first-order kinetics with respect to sebacic acid concentration in the kinetics regime. An increase in the molar ratio (G : SA) of the reactants decreased the average functionality of the system and the crosslinking density, resulting in the lowering of the activation energy and pre-exponential factor. The average functionality of the system had a profound effect on the crosslinking density, mechanical properties, and the reaction kinetics of the system. Three different PGS oligomers and films (PGS 0.6, PGS 0.8, PGS 1.0) were thoroughly characterised using Fourier transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS), wide angle X-ray scattering (WAXS), differential scanning calorimetry (DSC), and contact angle measurements. FTIR spectra of PGS oligomers confirmed the formation of ester bonds (1740 cm -1). Quantification of various functional groups in PGS films using XPS was in agreement with the theoretical values of the proposed structure. WAXS results indicated that PGS system with a higher average functionality possesses a higher degree of crystallinity. Crystallisation exotherms and melting endotherms of PGS systems revealed that the average functionality influences the density of crosslinking, degree of crystallinity, and the network structure of bioelastomers. Contact angle studies confirmed that an increase in the average functionality of PGS system increases hydrophilicity, and the surface treatment through aminolysis further increases the hydrophilicity of the films. Batch studies were performed on a Brabender Plasticorder®. The samples collected over a reaction period of 5 h were characterised using Fourier transform infrared spectroscopy (FTIR) and differential scanning calorimetry (DSC). The number-average molecular weight (Mn) and the weight-average molecular weight (Mw) of the oligoesters were determined using matrix-assisted laser desroption/ionization time-of-flight spectroscopy (MALDI-TOF) and compared with the corresponding values from the benchtop synthesis. It was found that due to higher shear-mixing and better orientation of functional groups, the degree of polymerisation at any stage of the reaction was higher in the Brabender than in the benchtop process. The gel-point of the reaction was determined from the crossover point of storage and loss moduli, and the reaction rate constant was calculated using the torque vs time data of the rheometer. The kinetics rate constant and the extent of the reaction in the Brabender were found to be higher than the corresponding values obtained from the conventional benchtop process by a factor of 2. PGS was found to be thermo-mouldable and adaptable to high-shear mixing, and hence is a better candidate for making thermoplastic elastomers using reactive extrusion. The challenges and possibilities in scaling up a batch process to a continuous process were investigated. The use of a wiped film reactor or a disk reactor along with reactive extrusion and batch-mixing (as a post-extrusion operation) is a commercially viable method to synthesise PGS oligomers. Such a continuous process will boost the production of bioelastomers for tissue engineering application by addressing the constraints in step-growth polymerisation. Finally, the effect of PGS substrate stiffness and surface treatment (aminolysis, hydrolysis, layer-by-layer deposition) on the morphology and lineage of mesenchymal stem cells – which have a capacity to differentiate themselves into cartilage, adipose, tendon, and muscle tissues – was analysed using fluorescence microscopy and DNA and protein assays. Stiffness of the PGS surface and the method of treatment influenced the cell attachment and spreading on different surfaces. However, cells did not differentiate into definite phenotypes at the end of 14 d time-point, indicating that higher time-points are needed to be considered to study the effect of matrix stiffness and surface treatment on cell attachment and phenotype differentiation.

Generating samples from multivariate distributions efficiently is an important task in Monte Carlo integration and many other stochastic simulation problems. Markov chain Monte Carlo has been shown to be very efficient compared to "conventional methods", especially when many dimensions are involved. In this article we propose a Hit-and-Run sampler in combination with the Ratio-of-Uniforms method. We show that it is well suited for an algorithm to generate points from quite arbitrary distributions, which include all log-concave distributions. The algorithm works automatically in the sense that only the mode (or an approximation of it) and an oracle is required, i.e., a subroutine that returns the value of the density function at any point x. We show that the number of evaluations of the density increases slowly with dimension. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

We use inequalities to design short universal algorithms that can be used to generate random variates from large classes of univariate continuous or discrete distributions (including all log-concave distributions). The expected time is uniformly bounded over all these distributions. The algorithms can be implemented in a few lines of high level language code. In opposition to other black-box algorithms hardly any setup step is required and thus it is superior in the changing parameter case. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

In the last years multilevel preconditioners like BPX became more and more popular for solving second-order elliptic finite element discretizations by iterative methods. P. Oswald has adapted these methods for discretizations of the fourth order biharmonic problem by rectangular conforming Bogner-Fox-Schmidt elements and nonconforming Adini elements and has derived optimal estimates for the condition numbers of the preconditioned linear systems. In this paper we generalize the results from Oswald to the construction of BPX and Multilevel Diagonal Scaling (MDS-BPX) preconditioners for the elasticity problem of thin smooth shells of arbitrary forms where we use Koiter's equations of equilibrium for an homogeneous and isotropic thin shell, clamped on a part of its boundary and loaded by a resultant on its middle surface. We use the two discretizations mentioned above and the preconditioned conjugate gradient method as iterative method. The parallelization concept is based on a non-overlapping domain decomposition data structure. We describe the implementations of the multilevel preconditioners. Finally, we show numerical results for some classes of shells like plates, cylinders, and hyperboloids.

In this paper we describe a version of transformed density rejection that requires less uniform random numbers. Random variates below the squeeze are generated by inversion. For the expensive part between squeeze and density an algorithm that uses a coverering with triangles is introduced. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

We use inequalities to design short universal algorithms that can be used to generate random variates from large classes of univariate continuous or discrete distributions (including all log-concave distributions). The expected time is uniformly bounded over all these distributions for a particular generator. The algorithms can be implemented in a few lines of high level language code. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Let G be a connected graph with n vertices and let x=(x1, ..., xn) be a real vector. A positive (negative) sign graph of the vector x is a maximal connected subgraph of G on vertices xi>0 (xi<0). For an eigenvalue of a generalized Laplacian of a tree: We characterize the maximal number of sign graphs of an eigenvector. We give an O(n2) time algorithm to find an eigenvector with maximum number of sign graphs and we show that finding an eigenvector with minimum number of sign graphs is an NP-complete problem. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Der Elektrik/Elektronik- und der IT-Anteil steigt derzeit in den aktuellen Premium -Fahrzeugen stetig an. Durch den Verbau von immer mehr (hochvernetzten) Steuergeräten im Fahrzeug wird versucht, dem Wunsch der Kunden nach mehr Funktionalität, Sicherheit, etc. gerecht zu werden. Aufgrund der Komplexität und der großen Entwicklungssprünge sind jedoch die neuen Steuergeräte meistens nicht mehr kompatibel mit den Vorgänger-Steuergeräten. Hier ist ein großes Einsparpotenzial vorhanden und dies ist auch der Ansatzpunkt des Forschungsthemas ”CompA“ (Compatibility Analysis of Electronic Control Units), das in diesem Dokument beschrieben wird. Im Rahmen dieses Forschungsthemas wird eine Methode definiert, mit der zwei Steuergeräte auf Rückwärtskompatibilität untersucht werden können. Der Ansatz baut auf drei Schwerpunkten auf: • Definition eines Spezifikationsansatzes zur hinreichenden Beschreibung von Steuergeräten auf Basis eines XML-Schemas. Es werden hierbei sowohl die statischen als auch die dynamischen Eigenschaften abgebildet. Dieser neuartige Spezifikationsansatz bildet die Basis für den nächsten Schwerpunkt. • Definition einer Methode zur Analyse von Rückwärtskompatibilität von Steuergeräten auf Basis eines XML-Schemas. Die Rückwärtskompatibilität zweier Steuergeräte bzw. Systeme wird auf Basis der zugehörigen XML-Dokumente analysiert. Kern der Vergleichsmethode ist hierbei ein effizientes Mapping der XML-Dokumente und ein Experten-Regelwerk. • Definition einer Methode zur Kompatibilitätsanalyse von Message Sequence Charts (MSC). MSCs werden eingesetzt, um dynamisches Verhalten an der Schnittstelle von Steuergeräten zu beschreiben. In diesem Dokument wird ein Ansatz definiert, mit dem MSCs zueinander auf Rückwärtskompatibilität geprüft werden können. Der Vergleich erfolgt auf Basis deterministischer Automaten. Des Weiteren wird im vorliegenden Dokument ein Konzept für eine graphische Benutzeroberfläche (GUI) vorgestellt, die zur Spezifikation von Steuergeräten geeignet ist und sich adaptiv unterschiedlichen Schemata anpasst. Alle vorgestellten Konzepte wurden in einem Software-Tool implementiert und die Gültigkeit an mehreren Beispielen validiert.

Perfect slice sampling is a method to turn Markov Chain Monte Carlo (MCMC) samplers into exact generators for independent random variates. The originally proposed method is rather slow and thus several improvements have been suggested. However, two of them are erroneous. In this article we give a short introduction to perfect slice sampling, point out incorrect methods, and give a new improved version of the original algorithm. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

This thesis is a multi-sited survey providing insight into integral performing arts institutions and how they engage in the distribution of cosmopolitan cultural capital to middlebrow audiences. It additionally provides a taxonomy of the different types of performances present across three sites: MSC OPAS, Arts Midwest, and the Association of Performing Arts Presenters’ Annual Conference in New York (APAP/NYC). My research methods include ethnography, interviewing, and textual analysis, but my investigation of these sites began with several leading questions: How do audiences read live performances for cosmopolitanism? How is that cosmopolitanism produced in key performing arts organizations? How is performance both a product that is marketed to venues and audiences and the means of marketing itself? Cosmopolitanism is an integral component to marketing, delivering, and enjoying live touring commercial performances. Performing arts presenters like OPAS, and presenting organizations, including Arts Midwest and APAP, engage cosmopolitanism on multiple levels as they work to provide regional audiences with otherwise unattainable “world-class” performances. Cosmopolitanism is present and presented every step of the way and the industry continues to advance cosmopolitan goals. This works shifts from analyzing cosmopolitan tourists to understanding touring cosmopolitanism because touring performances provide cosmopolitan cultural capital to community audiences located outside these urban centers. Touring performances provide opportunities for residents outside large metropolitan areas to engage in a global culture of performance and insert themselves into an imagined community of cosmopolitans. This is due in part to touring artists who deliver “world-class” performances to audiences that would otherwise entirely lack a connection to arts opportunities that accompany metropolitan centers and cosmopolitan communities. Cosmopolitanism is operationalized in performances of rurality, organizational culture and sociability, and exoticizing marketing strategies. I not only explore how cosmopolitanism is operationalized across these sites, but also how performance, in several of its variations, is operationalized, negotiated, and, of course, presented. More specifically, I examine artistic, interpersonal, organizational, and economic performances, as they are present across the three sites.